Observed log-chlorophyll at representative station for the St. Lucie Estuary

library(tidyverse)
library(lubridate)
library(mgcv)  
library(plotly)
library(WRTDStidal)
library(gridExtra)
source('R/funcs.R')

# format the data to model
data(sl_dat)
sl_mod <- sl_dat %>%
  rename(date = Date) %>% 
  mutate(
    doy = yday(date), 
    dec_time = decimal_date(date), 
    yr = year(date),
    mo = month(date, label = T)
  ) %>% 
  mutate(
    flo = sal, 
    lnchl = log(1 + chl)
    ) %>% 
  select(-sal)

# plot, all
p <- ggplot(sl_mod, aes(x = date, y = lnchl)) + 
  geom_line() +
  theme_bw() 
ggplotly(p)
# boxplot, by years
p <- ggplot(sl_mod, aes(x = yr, y = lnchl)) + 
  geom_boxplot() + 
  theme_bw()
ggplotly(p)
# boxplot, by month
p <- ggplot(sl_mod, aes(x = mo, y = lnchl)) + 
  geom_boxplot() + 
  theme_bw()
ggplotly(p)

Some simple GAMs to explore annual, seasonal trends.

# smooths to evaluate
smths <- c(
  "s(dec_time, bs = 'tp')",  
  "s(doy, bs = 'cc')",
  "te(dec_time, doy, bs = c('tp', 'cc'))"
)

# get all combinations of smoothers to model, one to many
frms <- list()
for(i in seq_along(smths)){
  
 frm <- combn(smths, i) %>%
    apply(2, function(x){
      paste(x, collapse = ' + ') %>% 
        paste('lnchl ~ ', .) %>% 
        formula
    }) 
  
 frms <- c(frms, frm)
 
}

# create models from smooth formula combinations
mods <- map(frms, function(frm){
  
  gam(frm, 
    knots = list(doy = c(1, 366)),
    data = sl_mod, 
    na.action = na.exclude
  )

})
names(mods) <- paste0('mod', seq_along(mods))

Summary stats of annual, seasonal models:

# smoother stats of GAMs
map(mods, ~ summary(.x)$s.table %>% data.frame %>% rownames_to_column('smoother')) %>% 
  enframe %>% 
  unnest %>% 
  kable
name smoother edf Ref.df F p.value
mod1 s(dec_time) 1.6461621 2.048370 9.7038674 0.0000678
mod2 s(doy) 4.0986733 8.000000 6.8154674 0.0000000
mod3 te(dec_time,doy) 9.9947633 12.933682 5.5626179 0.0000000
mod4 s(dec_time) 1.9430775 2.429282 8.9065355 0.0000567
mod4 s(doy) 4.1145399 8.000000 7.0520936 0.0000000
mod5 s(dec_time) 5.9855784 7.226382 2.1270530 0.0369088
mod5 te(dec_time,doy) 12.3369743 15.000000 4.0303044 0.0000000
mod6 s(doy) 4.0464881 8.000000 6.3773815 0.0000000
mod6 te(dec_time,doy) 2.4100580 3.304212 6.7570411 0.0001249
mod7 s(dec_time) 1.9175106 2.397382 9.0127722 0.0000550
mod7 s(doy) 4.1236170 8.000000 7.0552277 0.0000000
mod7 te(dec_time,doy) 0.0000065 15.000000 0.0000004 0.3651312 
# summary stats of GAMs
map(mods, ~ data.frame(
    AIC = AIC(.x), 
    R2 = summary(.x)$r.sq)) %>% 
  enframe %>% 
  unnest %>% 
  kable
name AIC R2
mod1 683.2360 0.0500261
mod2 653.5304 0.1302894
mod3 643.6646 0.1668405
mod4 634.5680 0.1787925
mod5 644.2521 0.1835579
mod6 634.4836 0.1798639
mod7 634.5693 0.1787532 
pred_dat <- sl_mod

# predictions
sl_res <- map(mods, function(x){
  pred_dat %>% 
    mutate(
      pred = predict(x, newdata = pred_dat)
    )
  }) %>% 
  enframe('mods') %>% 
  unnest

# plot
p <- ggplot(sl_res, aes(x = date)) + 
  geom_point(data = sl_mod, aes(y = lnchl), size = 0.5) + 
  geom_line(aes(y = pred, colour = mods)) + 
  theme_bw() + 
  theme(
    legend.position = 'top', 
    legend.title = element_blank()
    )
ggplotly(p)
# plot
p <- ggplot(sl_res, aes(x = doy, group = factor(yr), colour = yr)) + 
  geom_line(aes(y = pred)) + 
  theme_bw() + 
  theme(
    legend.position = 'top', 
    legend.title = element_blank()
    ) + 
  facet_wrap(~ mods, ncol = 2)
ggplotly(p)

Adding flow data to the model:

# smooths to evaluate
smths <- c(
  "s(dec_time, bs = 'tp')",  
  "s(doy, bs = 'cc')",
  "s(flo, bs = 'tp')",
  "te(flo, doy, bs = c('tp', 'cc'))", 
  "te(flo, dec_time, bs = c('tp', 'tp'))",
  "te(dec_time, doy, bs = c('tp', 'cc'))",
  "te(dec_time, doy, flo, bs = c('tp', 'cc', 'tp'))"
)

# get all combinations of smoothers to model, one to many
frms <- list()
for(i in seq_along(smths)){
  
 frm <- combn(smths, i) %>%
    apply(2, function(x){
      paste(x, collapse = ' + ') %>% 
        paste('lnchl ~ ', .) %>% 
        formula
    }) 
  
 frms <- c(frms, frm)
 
}

# create models from smooth formula combinations
mods2 <- map(frms, function(frm){
  
  gam(frm, 
    knots = list(doy = c(1, 366)),
    data = sl_mod, 
    na.action = na.exclude
  )

})
names(mods2) <- paste0('mod', seq_along(mods2))

Summary stats of best year/season model, year/season/flow model

# best model with only season, year
best1 <- map(mods,  AIC) %>% 
  unlist %>% 
  which.min %>% 
  mods[[.]]

# best model with season, year, flow
best2 <- map(mods2, AIC) %>% 
  unlist %>% 
  which.min %>% 
  mods2[[.]] 

best <- list(best1 = best1, best2 = best2)

# smoother stats of GAMs
map(best, ~ summary(.x)$s.table %>% data.frame %>% rownames_to_column('smoother')) %>% 
  enframe %>% 
  unnest %>% 
  kable
name smoother edf Ref.df F p.value
best1 s(doy) 4.0464881 8.000000 6.3773815 0.0000000
best1 te(dec_time,doy) 2.4100580 3.304212 6.7570411 0.0001249
best2 s(doy) 3.2726969 8.000000 5.4646634 0.0000000
best2 s(flo) 2.1261492 2.532475 1.1775041 0.2361336
best2 te(flo,doy) 0.9077802 13.000000 0.1933511 0.0154606
best2 te(flo,dec_time) 7.4271874 20.000000 1.0880301 0.0000178
best2 te(dec_time,doy) 0.5274598 8.000000 0.0673205 0.2037872
best2 te(dec_time,doy,flo) 12.3847743 48.000000 0.6027438 0.0000674 
# summary stats of GAMs
map(best, ~ data.frame(
    AIC = AIC(.x), 
    R2 = summary(.x)$r.sq)) %>% 
  enframe %>% 
  unnest %>% 
  kable
name AIC R2
best1 634.4836 0.1798639
best2 502.3692 0.3272847 
# predictions
sl_res2 <- map(best, function(x){
  pred_dat %>% 
    mutate(
      pred = predict(x, newdata = pred_dat)
    )
  }) %>% 
  enframe('mods') %>% 
  unnest

# plot
p <- ggplot(sl_res2, aes(x = date)) + 
  geom_point(data = sl_mod, aes(y = lnchl), size = 0.5) + 
  geom_line(aes(y = pred, colour = mods)) + 
  theme_bw() + 
  theme(
    legend.position = 'top', 
    legend.title = element_blank()
    )
ggplotly(p)
ptheme <- theme(
  axis.title.x = element_blank(), 
  axis.title.y = element_blank()
)
cols <- 'Spectral'
pb1 <- dynagam(best1, pred_dat, ncol = 1, col_vec = cols) + 
  ptheme + 
  theme(legend.position = 'none') +
  ggtitle('Best 1')
pb2 <- dynagam(best2, pred_dat, ncol = 1, col_vec = cols) + 
  ptheme + 
  ggtitle('Best2')
pleg <- g_legend(pb2)
pb2 <- pb2 + 
  theme(legend.position = 'none')

grid.arrange(
  pleg, 
  arrangeGrob(pb1, pb2, ncol = 2, bottom = 'lnQ', left = 'lnchl'), 
  ncol = 1, 
  heights = c(0.1, 1)
)